The "Dark Father" thing is just a coincidence, as the character was not turned into anyone's daddy until he began Empire Strikes Back. Originally it was just the name of various characters, not a "Sith Title" (as it became when he was writing Episode I, nearly 20 years later).

In-universe, how did Palpatine come up with the name? Your guess is as good as mine! I don't believe there is an official explanation...